Séminaire Lotharingien de Combinatoire, B61Ab (2009), 10 pp.

Bruce E. Sagan

Probabilistic Proofs of Hook Length Formulas Involving Trees

Abstract. Recently, Han discovered two formulas involving binary trees which have the interesting property that hooklengths appear as exponents. The purpose of this note is to give a probabilistic proof of one of Han's formulas. Yang has generalized Han's results to ordered trees. We show how the probabilistic approach can also be used in Yang's setting, as well as for a generalization of Han's formula in terms of certain infinite trees.

Received: June 11, 2008. Revised: January 19, 2009. Accepted: February 22, 2009.

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